Question

What is likely to be principal quantum number for a circular orbit of diameter 20 nm of the hydrogen atom, if we assume Bohr orbit be the same as that represented by the principal quantum number?

• A. 10
• B. 14
• C. 12
• D. 16

Answer 1

The correct option is B 14

The diameter is 20 nm. Hence, the radius is 10 nm or ${10}^{-8}m$. ......(1)

The radius of nth orbit is given by the expression $0.529\times {10}^{-10}\times n^2$. .....(2)

From (1) and (2)

$0.529\times {10}^{-10}\times n^2={10}^{-8}$

$n^2=189$

$n=13.75\approx 14$

Hence, the principal quantum number is 14.

Hence, the correct option is $B$